Final answer:
The centrosome is a critical microtubule-organizing center in animal cells and is involved in mitotic spindle formation, but it is not solely responsible for microtubule length dynamics, as plant cells that lack centrosomes and cells without centrosomes can still regulate microtubule length and undergo cell division.
Step-by-step explanation:
While the centrosome does play a significant role in microtubule organization in animal cells, it is not solely responsible for the rate of their lengthening and shortening.
Centrosomes, with their core components the centrioles, serve as major microtubule-organizing centers in animal cells and are crucial during cell division for the formation of the mitotic spindle. These structures help in pulling duplicated chromosomes apart during mitosis. However, the exact mechanism by which centrosomes might regulate the dynamics of microtubule length is not clear-cut. Microtubules themselves can both grow by adding tubulin subunits and shrink by losing them, and these processes can occur independently of the centrosome in certain contexts. Furthermore, plant cells, which lack centrosomes, and cells with removed centrosomes can still organize microtubules and undergo division.